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Table of Contents
Title
The music of MathProblem Scenario
I am trying to see if I can generate sound using fractal equations.
Broad Question
What are the effects of fractal generated sound will have on humans?Specific Question
Does fractal sound improve concentration as binaural sounds is claimed to?Hypothesis
When using a Julia set of equations the sound will effect the results of the test negatively vs. using Mandelbrot set equation generated sound.Independent Variable:
Two types of fractal generated audio.Dependent Variable:
Amount of puzzle complete.Variables That Need To Be Controlled:
Ambient noise in roomNo practice time
Vocabulary List That Needs Explanation
Audio: SoundFractal Design: A self similar graphical pattern plotted by a self similar equation
Self similar:In mathematics, a self-similar object is exactly or approximately similar to a part of itself.
Complex Number: Is a number that can be put in the form a + bi, where a and b are real numbers and i is the imaginary unit
General Plan
Have test subjects (students) in a room, one at a time, for ten minutes, to solve a 1000 piece puzzle while they're exposed to the extremely annoying noise generated by the fractal equations, then determine their performance by the number of properly placed pieces.
Potential Problems And Solutions
Person(s) must not have prior experience with this puzzleSafety Or Environmental Concerns
Audio level too damagingExperimental Design
Resources and Budget Table
Detailed Procedure
1. Obtain Chaos Pro2. Obtain Audio Paint
3. Generate A Fractal photo using Chaos Pro
4. Render the Fractal Image
5. Export The Fractal image to any given location
6. Open audio Paint
7. Import the fractal photo
8. Make length of the audio file TEN minutes.
9. Convert the Fractal Picture to Audio
10. Export sound
10. Obtain a puzzle
11. Obtain a person
12. Play music while person solves Puzzle
13. Record data
Time Line
2/26/13 Testing initiates in block 102/27/13 Testing concludes in block 10
Data Table
All Raw Data
Linked pieces/Total Pieces
40/1000
31/1000
13/1000
14/1000
8/1000
8/1000
67/1000
67/1000
8/1000
60/1000
80/1000
Graphs
What I could of done to improve this project
Larger test groupsSmaller puzzle w/ starting piece position consistent.
Smaller test window
Results
Students exposed to the Mandelbrot Set sound during the experiment performed better than those exposed to the Julia Set sound.Conclusion
The Julia set showed a higher degree of distraction to the subjects as indicated by both their performance and their comprehension to verbal cues during the experiment.Discussion
My results supported the project's initial hypothesis, which predicted that the Julia set of fractal sound/equations would affect the test results negatively vs. the Mandelbrot set which enhanced concentration. Though the data seems promising I do not believe results will be persistent since my test group was minusculeBenefit to Community and/or Science
It was my hope that given the growing evidence that there is a fractal relationship in all things, that maybe fractals might have a practical application to improve people's concentration.
Background Research
My background research took me many days, I had to learn what fractal equations were. I also had to get a grasp on what Complex numbers were. Inserting the SqRT of -1 into the fractal "Field" was difficult at first to understand but easier as time went on. A complex number is a way of putting (x,y) coordinates into one number with two parts. Usually consisting of a real number and an "Imaginary number" like SqRt of -1 = i.Once you understand why i = i Or why E=M(cc) fractal equations will make more sense. Conventional letters are key in mathematics due to limited space on most anything you would not want to write something that's large lengths unless needed. Abbreviations are awesome.
References
http://www.angelfire.com/art2/fractals/lesson2.htmAbstract
My project first started with a crazy idea. That was to use fractals to predict future outcome with a finite set of variables, like picking the winning lottery ticket number. There has been extensive research in fractal mathematics where fractal patterns emerge in seemingly random (chaos) data. The more I researched this, the more evident it was that doing so was beyond the abilities of an 8th grader with limited time. As I continued my research into fractals, I uncovered even more research that others had done revealing fractal patterns in problem solving binary trees. Viewing these patterns on the computer, I wondered what they would sound like if the pixels were changed to audio notes. Then, after listening to the various patterns, I was reminded of the binaurial sounds that are claimed to improve concentration or focus. So I wondered if I could do a performance-based experiment comparing two of these sounds and if either would have a positive or negative influence on the test subjects.